Transcript 8.1 Factoring Monomials

Lesson 8-1
Monomials and Factoring
p. 471
Some definitions
 Remember that a factor is a number that is multiplied
 The factors of a number are all the numbers that can
be multiplied to get that number
 One is a factor of every number
 Every number is always a factor of itself
Ex. Find the factors of 12.
1,2,3,4,6,12
 Prime Number – A whole number greater than one,
whose only factors are one and itself.
 Composite Number – A whole number greater than
one that has more than two factors
Factors
Find the factors of each number, then write if it
is prime or composite.
1. 36
1,2,3,4,6,9,12,18,36
composite
2. 23
1,23
prime
Prime Factorization
 A number can be expressed as a product of its prime
factors – this is prime factorization
 To find the prime factorization of a number, you can
use a factor tree.
Ex. Find the prime factorization of 90
90  2  3  3  5  2  32  5
 To find the prime factorization of a negative number,
start with negative 1
Ex. find the prime factorization of -140
140  1140
140  1 2  2  5  7  1 2 2  5  7
Factored Form
 A monomial is in factored form when it is
expressed as a prime factorization and the
variables are written out without exponents
Ex. Write each monomial in factored form
2  2  3 a  a  b  b  b
1. 12a 2b 3
2

66
pq
2.
1 2  3 11 p  q  q
Problems to Try
Find the factors of each number and classify as
prime or composite
1. 22
2. 31
Find the prime factorization of each number
3. 84
4. -132
Put each monomial in factored form
2
3 3

26rst
5. 18x y
6.
Greatest Common Factor (GCF)
 To find the GCF of two numbers:


Find the prime factorization of the two
numbers
Multiply the factors they have in common
Ex. Find the GCF of 48 and 60
1. Find the prime factorization 48  2  2  2  2  3
of each number
60  2  2  3  5
2. Circle common factors
3. Multiply the common factors
GCF  48,60  2  2  3  12
Examples
 Find the GCF of:
1. 15 and 16
15  3  5
16  2  2  2  2
GCF 15,16  1
If the two number have no common factors then the
GCF = 1.
The two numbers are called relatively prime.
2
2
36
x
y
and
54
xy
z
2.
36 x 2 y  2  2  3  3  x  x  y
54 xy 2 z  2  3  3  3  x  y  y  z


GCF 36 x y,54 xy z  18 xy
2
2
Example
 The area of a rectangle is 28 square inches.
If the length and width are both whole
numbers, what is the maximum perimeter of
the rectangle?
DRAW PICTURES TO SHOW YOU ALL
POSSIBILITIES!
The greatest perimeter is 58 inches.
Problems to Try
Find the GCF of:
1. 12 and 18
2.
27a 2b and 15ab 2c
3. Rene has crocheted 32 squares for an afghan. Each
square is 1 foot square. She is not sure how she
will arrange the squares but does know it will be
rectangular and have a ribbon trim. What is the
maximum amount of ribbon she might need to finish
the afghan?